... I assume Shawyer did not supply these equations in his papers as they are equations that should be known to microwave industry individuals skilled in the art. Anyway they are now in the public record....

I think you have done an outstanding job in discovering what Shawyer may have meant.

You are too humble in saying that these equations may be known in the art.

No, Shawyer's equations are NOT known to microwave industry individuals skilled in the art, because the overwhelming majority of microwave industry professionals do NOT use truncated cone cavities.

Shawyer makes a particular choice for lambdag1 and lambdag2 which is not found in the literature.He essentially models the truncated cone as two disjointed different cylinders: a cylinder corresponding to the big end and a cylinder corresponding to the small end. My intuition would have been to model the truncated cone instead as a single cylinder having a diameter equal to the Geometric Mean diameter, as done for example by @Notsosureofit for his model. (That's what I thought Shawyer had done and that's one reason why my interpretation of Shawyer's Design Factor was apparently not what he meant).

Shawyer's choice of modeling the truncated cone as two different cylinders with lambdag1 and lambdag2 may be a stroke of intuitive genius, or it may be flawed, that remains to be shown by your (and others) replications.But his choice of lambdag1 and lambdag2 is anything but obvious to me (*), it is never made explicit in his writings, and its validity remains to be proven

____________(*) Modeling a truncated cone as two disjointed cylinders is not only not obvious but it presents big theoretical problems in the limit as the small diameter goes to zero as essentially Shawyer models the pointy cone as a cylinder and a line. Again it maybe a great engineering approximation (or not), it remains to be proven.

Today i did the first test with the Emdrive (microwave oven magnetron and cooper frustum) The setup (magnetron and frusum) was suspended in a pendulum. I applied power for 40 Seconds with no visible thrust. Tomorrow will will try again with the magnetron on the small side. You have any suggestion for what should be the distance from the small side?After this i will adjust the power to the filament of magnetron and the frequency.To fine adjust the frequency i thought i can put 2 coils over the magnetron magnets to modify the magnetic field.My website;http://www.masinaelectrica.com/emdrive-independent-test/

Hey great job BTW. While I was out driving I was thinking of you and had a couple ideas. If you're willing would you/could you try:

1) Set the whole apparatus in motion, like a swing or a pendulum and measure the period while it is turned off. Then measure the period again while turned on. See if the period changes.2) If you have a way of measuring this, could you see if it is any easier or harder to displace the frustum from when it is turned off and then turned on. Any difference?

My calculations only assume Maxwell's linear equations. EW has a dielectric inside and they measured very small forces and very low temperatures.

Keep thinking and challenging all assumptions:

Because the Chinese (Prof. Yang's) measurements with embedded thermocouples show the OPPOSITE of NASA Eagleworks, in agreement with your expectation: the small end is much hotter

Prof. Juan Yang's reported temperature vs. time measurements with embedded thermocouples throughout their EM Drive cavity (without a polymer dielectric insert) under atmospheric conditions, that, curiously, show the highest temperature at the center of the small base (trace #1), followed, at a significantly lower temperature by the temperature at the periphery of the big base (trace #5).

My calculations only assume Maxwell's linear equations. EW has a dielectric inside and they measured very small forces and very low temperatures.

Keep thinking and challenging all assumptions:

Because the Chinese (Prof. Yang's) measurements with embedded thermocouples show the OPPOSITE of NASA Eagleworks, in agreement with your expectation: the small end is much hotter

Prof. Juan Yang's reported temperature vs. time measurements with embedded thermocouples throughout their EM Drive cavity (without a polymer dielectric insert) under atmospheric conditions, that, curiously, show the highest temperature at the center of the small base (trace #1), followed, at a significantly lower temperature by the temperature at the periphery of the big base (trace #5).

Take a look at the temperatures measured by the thermocouple Trace #1

I'm not sure what that would mean at this point.

Anyway, 2GHz is much less than the cosmic background temp. which is ~160GHz peak.

For the statistical mechanics among us, Q comes in w/ the partition function of the almost monochromatic photon spectra.

@Rodal: You say that you get a blow-up with your Df formula, and yeta) you agree that both lambdag1,2 are greater than lambda0 (because vg < c)b) you agree that, this being the case, it's mathematically impossible to get blow-up (denominator zero)

@Rodal: You say that you get a blow-up with your Df formula, and yeta) you agree that both lambdag1,2 are greater than lambda0 (because vg < c)b) you agree that, this being the case, it's mathematically impossible to get blow-up (denominator zero)

Clarify please?

You are thinking correctly, as a physical situation, as if lambda0 and lambdag1,2 are wavelengths occurring at a particular point in time and space.

However, the mathematical relationship between lambda0 and lambdag1,2, as defined above, is only physically correct for frequencies above the cutoff frequency.

For frequencies below the cutoff , the Design Factor blows up, at the value I gave in my post.

You can verify that this blow up only occurs at frequencies below the cut off .

The cutoff is chosen at the lowest natural frequency.

There are no standing waves in a cavity below the lowest natural frequency.

EDIT: More technically correct is to state that the Design Factor has a singularity: it becomes non-real (Imaginary) at that frequency.

The Design Factor has a singularity (due to the cut-off frequencies) starting at the cut-off frequency associated with the small diameter

We'll eventually look to start a Thread 3 - based on the timing of the next update of interest. That'll be up to the main contributors to decide that point as this thread is loooooooooooong and now coming up to 900,000 views (yikes).

Thread 3 will be constructed with an opening post that will be a quick look overview (article, previous threads, wiki and so on).

Have modified my Shawyer Df calculator and best Df scanner as per the derived Shawyer Df equation, using cutoff wavelength and guide wavelength as per microwave industry supplied equations. I assume Shawyer did not supply these equations in his papers as they are equations that should be known to microwave industry individuals skilled in the art. Anyway they are now in the public record.

The scanner still sweeps the frequency range 0Hz to 10GHz but reports the frequency that generates a Df as close to 1 as possible but not over.

The attached results are very interesting as the frequency needed to get the Df to just below 1 is very close to the Rf driving frequency used to generate Lambda0 or free wavelength in the selected medium.

While I'm still testing the spreadsheet, which meets both of Shawyers boundary conditions, the results for my Flight Thruster design are looking to be very close to what I could build. Bit of dimension tweaking should get the Df 1 frequency to the 3.85GHz Shawyer used.

Will post the spreadsheet after a bit more testing.

I've built and tested many microwave cavities over many years.

You're guided wavelength equation is wrong, because this is for a rectangular wave guide (i.e., not even a rectangular cavity)

You need to derive mode of frequency yourself (unless there is a paper somewhere) for a circular tapered cavity. There is no other way around it. I would start with Balanis - Advanced Engineering Electromagnetics as he derives a few examples for other topologies. Right now everything you are doing is wrong because you don't understand the physics. I would study that book from front to cover if I were you.

Also, to the guy operating the microwave magnetron outside of the microwave: STOPAt best you are violating the laws of your local government's regulatory committee for the electromagnetic spectrum. At worst you will damage your body. At this frequency, the damage is somewhat insidious. Due to low water content of your skin, you don't feel the heat, but internal nerve endings can be damaged so that chronic phantom pain can appear. Sometimes days after exposure. Please STOP otherwise you will inevitably be reported to your government.

You're guided wavelength equation is wrong, because this is for a rectangular wave guide (i.e., not even a rectangular cavity)

...

You are correct: Shawyer uses a number of references for open waveguides instead of closed cavities. For example, his main reference is Cullen's Ph.D. thesis published in the early '50s. When reading Cullen's paper I was surprised to find out that Cullen had used an OPEN waveguide (it had a transparent glass at one end, transparent to microwaves on purpose) to experimentally measure the pressure on the other end (where waves are reflected) of an open cylindrical waveguide. Not a truncated cone closed cavity.

Shawyer essentially models the closed truncated cone cavity as being two disjointed open waveguides. Having brought this up a number of times, only results in Shawyer providing a number of references and texts that don't support his approximation. His approximation is not obvious (at least to me), it is unsupported, and basically remains to be proven.

The anti-theoretical, heuristic, hands-on practical approach is to build a cavity and sweep through a likely frequency range while feeding it. Monitoring the match with a simple AC voltmeter will show dips, which will correspond to the various modes. Pick a few, use them in experiments. Viola

I've been trying to wrap my brain around why a difference in phase results in a better thrust. Also, why couldn't EW obtain a thrust without a dielectric?

I think we can all agree that in order for a net thrust, the momentum delivered to the larger end plate is smaller than that delivered to the smaller end plate. So where did the momentum go?

Can momentum be delivered and removed from an orbiting electron?

Take a simple two dimensional case with two atoms, one on the small end, one on the large end, each with their own electron orbiting at a the same angular frequency. If a force is applied to both of them, one in the direction of revolution and the other opposite, one of the forces would slow down the electron and the other would speed it up. The sped up electron requires a larger force to keep it tied to the nucleus and we have a net thrust.

Perhaps this could help explain a couple things:

The dielectric is composed of different elements, thus the electrons are orbiting at a different angular velocity. Using a constant frequency with different elements gives a certain degree of difference in the phase at which momentum is delivered to the electrons.

Shawyer observed more losses with a dielectric because a magnetron outputs a signal at many phases and somehow 'matches' the orbital tendency of the electrons. I imagine the magnetic component of the wave could be contributing to an alignment of electrons which could amplify this miniscule effect.

Any thoughts?

I'm digging through this paper right now and it seems to offer an answer to your question. I'll re-read it several times, as it's looking to be the Tar Baby in the Brier Patch for me.http://arxiv.org/pdf/1011.4376.pdf

Also, to the guy operating the microwave magnetron outside of the microwave: STOPAt best you are violating the laws of your local government's regulatory committee for the electromagnetic spectrum. At worst you will damage your body. At this frequency, the damage is somewhat insidious. Due to low water content of your skin, you don't feel the heat, but internal nerve endings can be damaged so that chronic phantom pain can appear. Sometimes days after exposure. Please STOP otherwise you will inevitably be reported to your government.

While I agree with your safety suggestions, I think your tone and delivery are a bit over the top. Microwaves are easily contained.

I'm digging through this paper right now and it seems to offer an answer to your question. I'll re-read it several times, as it's looking to be the Tar Baby in the Brier Patch for me.http://arxiv.org/pdf/1011.4376.pdf

I find it disheartening how much smaller is the effect explored in this "Tar Baby in the Brier Patch" paper and van Tiggelen's other papers, compared to what is claimed by the EM Drive researchers (particularly what is claimed by Shawyer and Prof. Yang regarding measured forces), and the fact that Shawyer and Prof. Yang do not use any dielectric polymer insert in their tests.

I had a look through the paper and am surprised the effect exists at all. Can someone explain where the opposite momentum goes?

I'm surprised that you are not asking: if indeed one can obtain this momentum (however little teeny tiny) by interacting with the QV, does that mean that one can obtain energy (however little teeny tiny) from the QV, and therefore there is a paradox ?

One unanswered question I had, as I put my engineers build spreadsheet together, was what effect does cavity length have on operation as the Shawyer Df equation does not use cavity length?

Then I found the attached and it all fell into place.

Then added the ability to calc the length resonance wavelength / frequency and guess what? The Flight Thruster specs, as worked on on this thread, say the length is resonate at close to 2x the wavelength of the applied 3.85GHz Rf signal. Did a bit of length tweaking and how have the length resonate at 1/2 the applied Rf frequency or 2x the applied wavelength.

...I can feel your pain, understand your concern and yes it concerns me too.I'm digging through this paper right now and it seems to offer an answer. I'll re-read it several times, as it's looking to be the Tar Baby in the Brier Patch for me.http://arxiv.org/pdf/1011.4376.pdf

I find it disheartening how much smaller is the effect explored in this "Tar Baby in the Brier Patch" paper and van Tiggelen's other papers, compared to what is claimed by the EM Drive researchers (particularly what is claimed by Shawyer and Prof. Yang regarding measured forces), and the fact that Shawyer and Prof. Yang do not use any dielectric polymer insert in their tests.

I understand the concern, I really do and it worries me too. There might be more than one way. I'm looking for the connection(s) and commonality in all.

It's hard to glean information from the other tests, I see what's going on right now in setting the cavity sizes and selecting correct harmonics (good detective work BTW) from the lack of information. Your tests were the only one where I feel confident that you used and reported a Dielectric Polymer with a solid yea/nay, it works, it doesn't. On a side note in my business of building Semiconductor machines (sold it and retired in 08 btw) I received sheet metals (copper included) with very thin coatings of plastic sheeting that needed to be pealed off, did I get it all before using, did some adhere, bonding to the surface affecting the tests? I'm not sure as that info isn't there.

This paper looks like it may offer out a way to the issues of violation of CoE and CoM which is a severe no no. As to the difference between the tests we simply have to do some more detective work. I think the answers are there.

Have modified my Shawyer Df calculator and best Df scanner as per the derived Shawyer Df equation, using cutoff wavelength and guide wavelength as per microwave industry supplied equations. I assume Shawyer did not supply these equations in his papers as they are equations that should be known to microwave industry individuals skilled in the art. Anyway they are now in the public record.

The scanner still sweeps the frequency range 0Hz to 10GHz but reports the frequency that generates a Df as close to 1 as possible but not over.

The attached results are very interesting as the frequency needed to get the Df to just below 1 is very close to the Rf driving frequency used to generate Lambda0 or free wavelength in the selected medium.

While I'm still testing the spreadsheet, which meets both of Shawyers boundary conditions, the results for my Flight Thruster design are looking to be very close to what I could build. Bit of dimension tweaking should get the Df 1 frequency to the 3.85GHz Shawyer used.

Will post the spreadsheet after a bit more testing.

I've built and tested many microwave cavities over many years.

You're guided wavelength equation is wrong, because this is for a rectangular wave guide (i.e., not even a rectangular cavity)

You need to derive mode of frequency yourself (unless there is a paper somewhere) for a circular tapered cavity. There is no other way around it. I would start with Balanis - Advanced Engineering Electromagnetics as he derives a few examples for other topologies. Right now everything you are doing is wrong because you don't understand the physics. I would study that book from front to cover if I were you.

The Guide Wavelength equation uses a circular cutoff wavelength as it's basis. That cutoff wavelength used is for the end conditions, just before reflection. It only focuses on that happens at each end.

A rectangular waveguide will have a different cutoff wavelength and hence a different Guide Wavelength.

As an ex ham, I see this as 2 semi connected resonate elements of an antenna. Each element has it's own unique operational characteristics as do each of the ends.

The length between the 2 ends is tuned to be at resonance of some sub, prime or harmonic of the Rf driving frequency as Shawyer says in the attachment.

My EM Drive design calculator says that for the Flight Thruster dimensions worked out on this thread, the length is very close to resonance at 2x the 3.85GHz wavelength and likewise the Df = 1 condition also occurs at close to the Rf driving frequency. I don't think this is a random event.

While I respect you may not agree with Shawyers or this analysis, I suggest that the Df =1 and length resonance results supporting operation at 3.85GHZ has added some degree of validity to the equation and calc process. At least for me.